The effect of the fish body on the source level and beam pattern of an acoustic fish tag signal was investigated through laboratory experiments and an analytical method. In laboratory experiments, the source level and beam pattern were measured in both a tag-only group and a tag-in-fish group. In the analytical method, both forward and backward scattering were calculated by assuming the acoustic tag was a point source and the swimbladder was an air-filled prolate spheroid. The mean source level of five tested tags decreased by ∼4 dB after implantation in fish bodies, which is important for designing fish migration studies using acoustic telemetry.

Monitoring fish migration is important to hydropower stakeholders like dam operators and fish biologists. Acoustic telemetry with injectable acoustic transmitters (often called acoustic tags) is an efficient way to monitor fish migration path and passage rate (Deng et al., 2017). Because tag size must be limited to minimize the effect of acoustic tags on fish behavior, the source level and detection range of acoustic tags are limited. Therefore, field experiments must be designed carefully to maximize the efficiency of fish tags. It is particularly important to understand how a fish's body affects the source level and beam pattern of the implanted tag.

When implanted in a fish, the tag and the body can be viewed as a single transmitter, and the beam pattern of the tag-fish system is affected mainly by scattering from the swimbladder and absorption by fish flesh. In a previous experiment, the importance of the swimbladder in acoustic backscattering by fish was evaluated by Foote (1980), who compared the target strengths of three gadoid species [Atlantic cod (Gadus morhua), saithe (Pollachius virens), and Atlantic pollock (Pollachius pollachius)] and Atlantic mackerel (Scornbet scombrus) (lack of a swimbladder). In another experiment with 12–14 cm yellow perch (Perca flavescens) (Sun et al., 1985), the swimbladder was found to contribute to about 80% of the back-scattered energy at 220 kHz, and invertebrae, head and flesh were distributed scatterers. In addition to the back scattering, the forward scattering by Japanese mackerel (Scomber japonicus) was also measured directly in laboratory experiments (Ding, 1997). In analytical and numerical models, the swimbladder has been approximated as a fluid-filled cylinder (Clay, 1991), a gas-filled prolate spheroid (Furusawa, 1988), and some other shapes and boundary conditions (Jech et al., 2015). In the case of acoustic tags for juvenile salmon (Oncorhynchus spp.) working at 416.7 kHz frequency (i.e., wavelength ∼0.0036 m) (McMichael et al., 2010), the swimbladder is located <0.01 m from the acoustic tag, and the incident waves cannot be approximated as plane waves. Moreover, both the backscattering and the forward scattering should be considered to fully understand the effect of fish body on the beam pattern.

The objective of this study is to understand the effect of the fish body on the source level and beam pattern of the fish tag through a set of laboratory experiments and an analytical method. The result serves as an attempt to maximize the efficiency of the fish tag, whose source level is difficult to enhance due to its size requirement and the battery longevity.

The experiment was conducted in a water tank (length 1.26 m, width 0.95 m, height 0.90 m) lined with anechoic materials (Aptflex F48, Precision Acoustics, Ltd, Dorchester, Dorset, UK) in the Bio-Acoustics and Flow Laboratory at Pacific Northwest National Laboratory (PNNL) (Deng et al., 2010) using acoustic tags manufactured at PNNL (Deng et al., 2015). The acoustic fish tag [Fig. 1(a)] was composed of a cylindrical piezoelectric transducer, a micro-battery, and an integrated circuit, with an operating frequency of 416.7 kHz and a pulse duration of 744 μs (McMichael et al., 2010). Two groups were designed for laboratory experiments: a tag-only group and a tag-in-fish group. For the tag-only group, five tags were randomly chosen among those that had a mean source level of at least 153 dB re 1 μPa at 1 m when the tag was oriented with the piezoelectric transducer towards the hydrophone. For the tag-in-fish group, five juvenile Chinook salmon (Oncorhynchus tshawytscha) were randomly selected from a pool that contained fish of similar size (more details about fish handling are included in the supplementary material1). The mean and the standard error of the fork length of the five fish were 101.6 and 2.2 mm, respectively. The fish samples were euthanized before the experiment. Necropsies after the beam pattern measurement showed that the swimbladders were in relatively full inflation. During the experiment in the acoustic tank, each fish was held using woven elastic bands 2.54 cm wide around the head and the tail separately. A weight was attached to each woven elastic band to ensure that buoyancy would not affect the tilt or the orientation of fish relative to the hydrophone [Fig. 1(b)]. The test with the tag-only group was performed by measuring the source level of the selected tags, whereas the test with the tag-in-fish group was performed by measuring the source level of the same tags after each tag was implanted in a fish. For both groups, the source level was measured by rotating the fish and tag clockwise over 360° with an increment of 10°, with a hydrophone placed 1 m from the tag [Fig. 1(c)]. The potential effect on scattering from the rigging or deformation of the fish caused by the setup was neglected.

Fig. 1.

(Color online) (a) The injectable acoustic transmitter for juvenile salmon. (b) An illustration of the setup of the tag-in-fish measurement. A weight was attached to each piece of woven elastic band to ensure that buoyancy would not affect the tilt or the orientation of fish relative to the hydrophone. (c) The experimental setup of the source level and beam pattern measurement in a water tank with anechoic materials.

Fig. 1.

(Color online) (a) The injectable acoustic transmitter for juvenile salmon. (b) An illustration of the setup of the tag-in-fish measurement. A weight was attached to each piece of woven elastic band to ensure that buoyancy would not affect the tilt or the orientation of fish relative to the hydrophone. (c) The experimental setup of the source level and beam pattern measurement in a water tank with anechoic materials.

Close modal

The tag message was a 31-bit code series modulated with binary phase-shift keying, where 0's and 1's in the binary code are represented by two phases in the carrier signal (McMichael et al., 2010). The first seven bits was a Barker code (1110010). The spectrum of the transmit signal has a main lobe centered around 417 kHz with a bandwidth of about 83 kHz. Data received by the hydrophone were first processed to extract the tag messages from raw data, i.e., the time of arrival of tag messages was first determined. The method used was to set a threshold with a rising edge in the waveform amplitude. Since the amplitude of received messages varied angularly, the threshold was set as half of the root mean square (rms) of the amplitude of the received Barker code, which is adaptive to the angular variation of signal amplitudes. With the time of arrival, tag messages were extracted at each angle. Then, the source level and beam pattern were calculated using the rms pressure amplitude of the Barker code at each angle. The Barker code was used to calculate the source levels since it is universal for all tags, while the remaining portion of the codes are unique for each tag.

The above data processing procedures were first applied to the tag-only group and the tag-in-fish group to extract tag messages of both groups from raw data. Then, based on the superposition principle of sound field, for each individual tag, tag messages of the tag-only group were coherently subtracted from the messages of the corresponding tag-in-fish group to obtain the scattered sound pressure by the fish body, using the same coherent subtraction processing as Ding (1997). Last, the levels of scattered pressure were calculated with the rms amplitudes of the seven-digit Barker codes. In both tag-only and tag-in-fish groups, tag messages were transmitted at least ten times at each angle for each tag. Sound source levels were first calculated for each time of transmission, and then the statistical mean of source levels was calculated among ten repetitive transmissions at each angle for each tag. Last, mean source levels at each angle were taken for the five tested tags.

In the analytical method, we assume that the swimbladder is an air-filled prolate spheroid and the acoustic tag is a point source. With this assumption, the multiple scattering between several scatterers is avoided. Although the assumption is unrealistic [tag-only beam patterns in Fig. 3(a) shows that the tag is not omnidirectional, although the transducer of the tag is omnidirectional], it simplifies the problem and makes it possible to analyze the scattering from the swimbladder alone. Note that the model covered only the swimbladder and neglected the scattering from other portions of fish body. Thus, the analytical results cannot be compared directly with the experimental results. Nevertheless, it helps understand the potential impact of the swimbladder on the beam pattern of the tag-fish system.

When the swimbladder is approximated by a prolate spheroid, the scattered field from the swimbladder and the incident field of the point source can be solved analytically in prolate spheroidal coordinates (Spence and Granger, 1951; Lauchle, 1975). A detailed explanation to the assumption of the tag and the swimbladder as well as the formulation of the analytical method are included in the supplementary material.1 In this study, an analytical and numerical model developed by Adelman et al. (2014a,b) in matlab (MathWorks, Inc., Natick, MA) is employed due to its open source convenience and less computational complexity compared to traditional finite element methods. The swimbladder was approximated by an air-filled prolate spheroid with a major axis length of 40 mm and a minor axis length of 9 mm. This geometry is based on necropsy of a fish and measurement of a swimbladder after the experiment (Fig. S1 in the supplementary material1). The surrounding medium including other portions of the fish body was assumed to be water for simplification, with the sound speed of 1480 m/s at room temperature and the attenuation coefficient of 0.038 dB/m at 416.7 kHz. The orientation of the swimbladder, the tag and the hydrophone were depicted in Fig. 2. The major axis of the swimbladder was set as the z-axis in Cartesian coordinates, and its center was located at (x0, y0, z0) = (0, 0, 0). Meanwhile, the point source, i.e., the center of the acoustic transducer, was located at (x1, y1, z1) = (−0.004, −0.004, 0.004) m. The hydrophone was located in the plane of y = −0.004 m at 1 m from (x1, y1, z1). The battery of the tag faced the fish head. The zero angle of the beam pattern corresponded to the orientation when the tag aligned with the hydrophone and the piezoelectric transducer faced the hydrophone. At 90° angle, the swimbladder was located between the tag and the hydrophone. Angles 0°–180° corresponded to forward scattering while angles 180°–360° corresponded to backscattering by the swimbladder. The scattered acoustic pressure and the total acoustic pressure was calculated using the tool of Adelman et al. Since the model requires the characteristic impedance of the boundary, which is unknown for the elastic layer of the swimbladder, both rigid and soft boundary conditions for the swimbladder were investigated instead. The analytical result on the plane defined by y = −0.004 at a distance of 1 m from the point source was obtained and was compared with the experimental result.

Fig. 2.

The orientation of the swimbladder, the acoustic tag and the hydrophone in the analytical model. At zero angle, the tag aligned with the hydrophone with the piezoelectric transducer facing the hydrophone.

Fig. 2.

The orientation of the swimbladder, the acoustic tag and the hydrophone in the analytical model. At zero angle, the tag aligned with the hydrophone with the piezoelectric transducer facing the hydrophone.

Close modal

The directivity of source levels of the tag-only and tag-in-fish groups [Fig. 3(a)] was calculated using the seven-digit Barker code of the extracted messages. Note that 0° is the direction where the orientation of the acoustic tag aligns with the hydrophone with the transducer facing the hydrophone (Fig. 2). Results in Fig. 3(a) are the mean levels of five samples at each angle. The standard deviation of source level measurements of five samples over all angles is 1.83 ± 1.43 dB and 3.80 ± 1.56 dB for the tag-only and tag-in-fish groups, respectively. Note that the directivity of the tag-only group is caused by the scattering from the tag circuit and battery, while the directivity of the tag-in-fish group is a combination of scattering by the fish body and the tag circuit/battery. From 340° to 190° in the counterclockwise direction, the source level of the tag-only group was 7.07 ± 5.51 dB higher than the tag-in-fish group, i.e., scattering from the swimbladder interfered destructively with signals radiated by the tag. From 200° to 330° with exception of 250°, 260°, 270°, and 280° in the counterclockwise direction, the source level of the tag-in-fish group was 3.83 ± 2.23 dB higher than in the tag-only group, due to constructive interference between tag-radiated signals and the backscattered signals. The interference between the scattered signal and the tag source signal is demonstrated at two representative angles in Fig. S2 of the supplemental material1.

Fig. 3.

(Color online) The source levels (in dB) measured in laboratory experiments. (a) The source levels of the tag-only group and the tag-in-fish group. (b) The levels of the tag-only group and the levels of the scattered signal by the fish body.

Fig. 3.

(Color online) The source levels (in dB) measured in laboratory experiments. (a) The source levels of the tag-only group and the tag-in-fish group. (b) The levels of the tag-only group and the levels of the scattered signal by the fish body.

Close modal

To further understand how the fish body affects the source level and beam pattern of the signals from the tag-in-fish group, the scattering levels from the fish body were obtained and then compared with the beam pattern of the tag-only group [Fig. 3(b)], following the coherent subtraction processing presented in Sec. 2.1. Recalling that the tag was assumed to be a point source, we focused on the difference between the levels of scattered signals and the tag-only source levels. By comparison, the scattering levels at 200°–230° were higher than those of the tag-only group by 3.84 ± 0.91 dB, while at other angles the scattering levels were lower than the tag-only levels by 4.26 ± 2.73 dB, i.e., the scattering level from the swimbladder had a peak at angles 200°–230°. Combining this with Fig. 3(a), forward scattering of the fish body interfered destructively with the tag source signal, while backscattering of the fish body interfered constructively with the tag source signal. These results illustrate how the fish body affects the source level and beam pattern of tags implanted into fish bodies. Note that the coherent subtraction cannot remove the multiple scattering between the tag and the fish body. Thus, the scattering beam pattern in Fig. 3(b) is not just the scattering by fish body; it also has the contribution from multiple scattering. While we did not directly measure the scattering from the fish body experimentally, the results are still useful for better understanding of the scattering.

Under the point source assumption, the levels of the scattered signals by the swimbladder with both the rigid and the soft boundary conditions for the swimbladder were obtained [Fig. 4(a)]. The source level of the point source was adjusted to 155 dB re 1 μPa at 1 m based on the mean value from the experiment with five tags at the angle of 0°. Between 0° and 180° in the counterclockwise direction, which indicates the configuration when the swimbladder is located between the fish tag and the hydrophone, the forward scattering with the soft boundary condition was stronger than that with the rigid boundary condition. The difference suggests that the use of the full analytical approach was appropriate, rather than using only backscattering. At angles from 200° to 250°, the scattering levels were higher than at other angles under both soft and rigid boundary conditions; this result was consistent with the experimental result [Fig. 3(b)]. The asymmetry of the scattering beam pattern in both analytical and experimental results indicated that the tag was not located on the minor axis of the spheroidal swimbladder.

Fig. 4.

(Color online) The source levels (in dB) obtained from the analytical model. (a) The levels of the scattered acoustic field by the swimbladder with rigid and soft boundary conditions of the swimbladder, when a point source is present. (b) The levels of the total sound pressure field.

Fig. 4.

(Color online) The source levels (in dB) obtained from the analytical model. (a) The levels of the scattered acoustic field by the swimbladder with rigid and soft boundary conditions of the swimbladder, when a point source is present. (b) The levels of the total sound pressure field.

Close modal

The source level due to the total pressure field [Fig. 4(b)] was calculated by summing the point source pressure field and the scattered pressure field. As discussed earlier, the analytical tag-only group showed a uniform beam pattern for all angles because the fish tag was modeled as a point source. The soft boundary condition produced a weakening of the source level of the tag-in-fish group relative to that of the point source between 340° and 190° in the counterclockwise directions. This result had very good consistency with experimental results in Fig. 3(a), where the tag-in-fish result also showed a weakening trend in the same directions. On the other hand, from 190° to 340° in the counterclockwise direction, the source level using a soft boundary had a strengthening trend relative to the point source, which partially overlapped with the experimental result. The rigid boundary condition also showed a weakening trend, in the 10°–160° directions, but the levels of weakening were much smaller than with the soft boundary condition.

Although the acoustic scattering model could not accurately quantify the complete effect of the fish body on the source level because the simplified model contained only the swimbladder, the model has qualitatively demonstrated the effect of the swimbladder on the fish tag directivity, which has certain consistency with laboratory experimental results. The results will play an important role in designing field experiments of fish tagging, where knowledge of the detection range of the acoustic fish tag is crucial in planning the layout of acoustic receivers. Based on the experimental results of five tested tags, the mean source level over all angles decreases from 147.6 dB re 1 μPa at 1 m to 143.7 dB re 1 μPa at 1 m after a tag is implanted in a fish body. Correspondingly, when the background noise level is 90 dB and the threshold of the signal-to-noise ratio for the detection of the tag is 6 dB, for an acoustic tag working at 416.7 kHz with absorption coefficient of 0.038 dB/m in water, the detection range decreases from 176 m to 135 m, assuming the sound pressure attenuates spherically.

While the experimental and analytical results are consistent in certain aspects, limitations should be noted in the analytical method: (1) the analytical model can only contain one scatterer; (2) the fish tag is modeled as a point source, which is not valid when the size of the piezoelectric transducer is on the same order as 0.0036 m, the wavelength of sound at 416.7 kHz in water, and (3) the boundary condition of the swimbladder is too ideal. For a future study, a finite element model based on multiphysics can be developed that overcomes these limitations.

This study demonstrated the effect of a surrounding fish body on the beam pattern of an acoustic fish tag in laboratory experiments using a tag-only group and a tag-in-fish group. The experimental results were combined with the results of an analytical model, which assumed that the tag was a point source and the swimbladder was a gas-filled prolate spheroid. Both experimental and analytical results showed that the fish body (with the swimbladder) caused a decrease of the source level in forward scattering directions, due to destructive interference between the tag source signal and the forward scattered signal. The mean source level of acoustic transmitters over all angles decreased by 4 dB after implantation in the fish body, which is an important reference for designing fish migration studies using acoustic telemetry.

This study was funded by the U.S. Army Corps of Engineers (USACE) and the U.S. Department of Energy (DOE) Water Power Technologies Office. We thank Brad Eppard and Scott Fielding from USACE and Dana McCoskey and Tim Welch from DOE.

1

See supplementary material at https://doi.org/10.1121/1.5112836 for details about fish handling, assumptions and formulation of the analytical method, and fish tag signals at two representative angles.

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Supplementary Material